Evolution__3rd_Edition

448 PART 4 / Evolution and Diversity
Box 15.2
Phylogenetic Inference by Maximum Likelihood
Real sequence data consist of nucleotides at a long series of sites. In
the calculations of maximum likelihood, each nucleotide site is
subject to much the same calculation and we can look at any one
site to see what the calculations are. Suppose we have one site and
four species (called 1, 2, 3, and 4) and their nucleotides are:
A 1
C 2
3 G
4 G
We now need a model of evolutionary change. The simplest is the
model shown in Box 15.1, in which the chance of changing from one
nucleotide to another is p. We can write out a matrix, with the
chance of changing from one state to another (per time unit):
Final state
A C G T
Initial state A 1 − 3p p p p
C p 1 − 3p p p
G p p 1 − 3p p
T p p p 1 − 3p
If the nucleotide is A, for instance, it has a chance 1 − 3p of
staying A and p each of changing into C, G, and T. Suppose that
each branch is one time unit long. We now calculate the probability
of observing the data for all possible states of the internal nodes.
We could start with:
A
C
G G
That is, we assume both internal nodes have G. The total chance
of this is p 2 * (1 − 3p)3 . In two of the branches there has been a
change (chance 1 − 3p). We calculate the same sort of probability
for all 16 possible combinations of the two nucleotides at the two
internal nodes. That gives us the total probability of observing the
data at this one site, given the model of evolution. Probabilities of
this sort tend to be very small and they are usually converted to
natural logarithms to make the numbers more manageable (so
21np + 3 ln (1 − 3p) can be written as ln p + 3 ln (1 − 3p).
In practice, we may have nucleotide data for 100 sites. The same
sort of calculation is performed for every site, to find the total
likelihood for the tree. We then need to do the same calculation for
all the other possible unrooted trees. The best estimate of the true
tree is taken to be the one with the highest probability (or maximum
likelihood) of being observed. With data such as we used for
parsimony in Figure 15.14, the result would usually be the same
with maximum likelihood. The trees that require more evolutionary
events will also be less probable, provided the value of p in the
model of evolutionary change is low.
Further reading: Swofford et al. (1996), Page & Holmes (1998),
Graur & Li (2000).
advantages, for instance it gives an exact probability for each unrooted tree, and this
makes quantitative comparisons between trees straightforward. We can say that one
tree is so many percent more probable than another. Quantitative comparisons of this
kind are not so easy with the technique of parsimony.
G
G
..